Browsing by Author "Park, Choonkil"

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Efficient scheme for a category of variable-order optimal control problems based on the sixth-kind Chebyshev polynomials
(de Gruyter Poland Sp Z O O, 2024) Sadri, Khadijeh; Hosseini, Kamyar; Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali; Park, Choonkil
The main goal of the present study is to introduce an operational collocation scheme based on sixth-kind Chebyshev polynomials (SCPs) to solve a category of optimal control problems involving a variable-order dynamical system (VODS). To achieve this goal, the collocation method based on SCPs, the pseudo-operational matrix for the fractional integral operator, and the dual operational matrix are adopted. More precisely, an algebraic equation is obtained instead of the objective function and a system of algebraic equation is derived instead of the VODS. The constrained equations obtained from joining the objective function to the VODS are ultimately optimized using the method of the Lagrange multipliers. Detailed convergence analysis of the suggested method is given as well. Four illustrative examples along with several tables and figures are formally provided to support the efficiency and preciseness of the numerical scheme.
Citation Count: 0
FRACTIONAL DYNAMICS OF CHRONIC LYMPHOCYTIC LEUKEMIA WITH THE EFFECT OF CHEMOIMMUNOTHERAPY TREATMENT
(World Scientific Publ Co Pte Ltd, 2024) Jan, Rashid; Salahshour, Soheıl; Alyobi, Sultan; Khan, Zaryab; Hosseini, Kamyar; Park, Choonkil; Paokanta, Siriluk
Currently, immunotherapy is seen to be the most effective cancer treatment. This is especially true while treating chronic lymphocytic leukemia (CLL), a slow-growing B-lymphocyte neoplasm that gradually compromises the immune system. Mathematical modeling is acknowledged as a key technique for analyzing theoretical and practical challenges in this field of cancer research and others. We were inspired to develop a mathematical model because of its dearth in investigations of chemotherapy-induced immunotherapy for CLL. This study effort formulates the dynamics of lymphocytic leukemia utilizing fractional calculus to conceptualize the complex processes of this viral illness. The basic idea of fractional calculus has been shown using the Atangana-Baleanu framework. For the suggested model's chaotic and dynamic behavior, a new numerical approach is described. We inspect the stability and convergence of the suggested numerical technique in our work. The fluctuation of various system input elements has demonstrated the oscillatory and chaotic behavior of the system. Moreover, we have demonstrated how the suggested mechanism of lymphocytic leukemia infection is affected by fractional order. Through numerical simulations, the most important input parameters are emphasized, and the policymakers are given control intervention suggestions.